Why are Disciplinary Practices in Mathematics Important as Learning Practices in School Mathematics?

In this paper, we discuss why it is important that the practices of school mathematics reflect the way mathematicians do mathematics; that is the thinking and practices in mathematics. One way to view the differences between mathematics and school mathematics is to describe them as disciplinary practices and learning practices following Cohen and Ball (2001). Consider for example justification and argumentation, these are disciplinary practices in mathematics, but in school mathematics these are learning practices. In mathematics justification and argumentation are disciplinary practices because they are the means by which mathematicians validate new mathematics. In school mathematics argumentation and justification are learning practices because they are the means by which students enhance their understanding of mathematics and their proficiency at doing mathematics. Thus, these practices are not just a desirable end product or outcome of a mathematics education; they are a means by which to learn and do mathematics. It is this aspect that we will take into consideration as we discuss the relationship between disciplinary mathematics and school mathematics. One of the overarching questions in the overview proposal for this ICMI Working Group is, “How do (should) the goals of school mathematics reflect the nature of disciplinary thinkin